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We parallelize density-matrix renormalization group to directly extend it to2-dimensional ($n$-leg) quantum lattice models. The parallelization is mademainly on the exact diagonalization for the superblock Hamiltonian since thepart requires an enormous memory space as the leg number $n$ increases. Thesuperblock Hamiltonian is divided into three parts, and the correspondentsuperblock vector is transformed into a matrix, whose elements are uniformlydistributed into processors. The parallel efficiency shows a high rate as thenumber of the states kept $m$ increases, and the eigenvalue converges withinonly a few sweeps in contrast to the multichain algorithm.

Direct Extension of Density-Matrix Renormalization Group toward  2-Dimensional Quantum Lattice Systems: Studies for Parallel Algorithm,  Accuracy, and Performance